The Robbins estimator is the most iconic and widely used procedure in the empirical Bayes literature for the Poisson model. On one hand, this method has been recently shown to be minimax optimal in terms of the regret (excess risk over the Bayesian oracle that knows the true prior) for various nonparametric classes of priors. On the other hand, it has been long recognized in practice that Robbins estimator lacks the desired smoothness and monotonicity of Bayes estimators and can be easily derailed by those data points that were rarely observed before. Based on the minimum-distance distance method, we propose a suite of empirical Bayes estimators, including the classical nonparametric maximum likelihood, that outperform the Robbins method in a variety of synthetic and real data sets and retain its optimality in terms of minimax regret.

翻译：罗宾斯估计量是经验贝叶斯文献中泊松模型最具代表性且广泛使用的程序。一方面，近期研究表明，对于各类非参数先验类，该方法在遗憾（即相对于已知真实先验的贝叶斯神谕的额外风险）意义上具有极小极大最优性。另一方面，实践中长期存在一个认识：罗宾斯估计量缺乏贝叶斯估计量所需的平滑性和单调性，且易因那些先前罕有观测的数据点而偏离。基于最小距离方法，我们提出了一系列经验贝叶斯估计量（包括经典的非参数最大似然估计）。这些估计量在多种合成数据集和真实数据集中均优于罗宾斯方法，且保持了其在极小极大遗憾意义上的最优性。